Various methods for the efficient computation of line spectral frequencies (LSFs) have been proposed to address the computationally intensive task of isolating the roots of high-order polynomials in linear predictive (LP) systems. An ASIC implementation of one such algorithm to compute LSFs has been developed, simulated and synthesized. The design, expressed entirely in VHDL, is intended for implementation into larger speech processing systems. The design developed is suitable for speech coding applications requiring a 10th order LP analysis and for speaker recognition applications which need a 12th order analysis. The resulting efficient design is of low complexity, modular, optimized for speed and area and can be used in larger speech processing systems to offload main application processors and DSPs. When the designed ASIC is part of a speaker identification system, the same accuracy as a software implementation is obtained.